In a wide range of industrial control systems, the value of a parameter of interest is maintained within a specified interval by first determining the transit time required for some phenomenon or process to travel a predetermined distance.
One example is shown in FIG. 1, which depicts a block diagram of a feedback system employed to control the flow rate of some substance or medium, such as pulverised coal or cooling fluid. The system comprises two suitable non-invasive sensors SX and SY, placed outside the flow pipe FP, a time-delay discriminator TDD, a control unit CON, and a suitable actuator ACT, such as a signal-controlled valve or pump.
In the case of pulverised coal, the sensors may, for example, detect time-varying changes in the electric charge carried by moving coal particles. In the case of determining the flow rate of coolant in, for example, a pressurised water reactor, the sensors will usually detect a γ-ray emitting element carried by the fluid. In either case, the sensors are responsive to an observed physical phenomenon varying in time in a noise-like fashion, and signals produced by the sensors are representations of that phenomenon.
The time-delay discriminator TDD processes two signals, x(t) and y(t), supplied by the sensors and determines the time delay (the transit time) Δ between those signals. Because the distance D between the sensors SX and SY is known, the required flow rate FR corresponds to some nominal value Δ0 of transit time, where Δ0=D/FR. The time-delay discriminator TDD provides at its output the value of a time-delay error ε=(Δ−Δ0), indicative of the discrepancy between the observed and the required flow rates.
The value of error ε provided by the time-delay discriminator TDD is then converted by the control unit CON into a suitable corrective signal applied to the actuator ACT. The main function of the actuator ACT is to adjust the actual flow rate in such a way as to nullify (or at least significantly reduce) the time-delay error ε, thereby attaining the required flow rate FR.
FIG. 2 shows an example of another feedback control system employed by an industrial robot ROB whose main function is to follow (‘shadow’) a moving vehicle MOV, while maintaining a specified ‘safe’ distance D. A similar control system can be used in automotive applications, for example, in collision-avoidance, cruise control or pre-crash vehicle conditioning.
The system comprises a transmitter TX driving a transmit element TE, a receive element RE coupled to a signal receiver RX, a transmit sensor SX, a receive sensor SY, a time-delay discriminator TDD, a control unit CON, and a drive control block ACT.
A wideband noise or chaotic signal generated by the transmitter TX is sent via the transmit element TE toward the preceding vehicle. The time-delay discriminator TDD processes jointly two signals: a copy of the transmitted signal x(t), captured by the transmit sensor SX, and a signal y(t) reflected back by the vehicle and applied to the receive sensor SY. The time-delay discriminator TDD determines the time delay Δ between the signals x(t) and y(t). Because the propagation velocity v of the transmitted and received signals is assumed to be known, the specified distance D will be maintained, if the observed delay time A is equal to its nominal value Δ0=2D/v.
Accordingly, the time-delay discriminator TDD provides at its output the value of a time-delay error ε=(Δ−Δ0), which is converted by the control unit CON into a corrective signal. This signal is then used by the drive control block ACT to adjust the robot's speed in such a way as to nullify (or at least significantly reduce) the time-delay error ε, thereby maintaining the required distance D.
The above two examples of applications involving a time-delay discriminator represent two classes of systems incorporating a delay-locked loop, described extensively in the prior art. In such systems, either the velocity or distance is being adjusted, while the other complementary parameter (distance or velocity) is constant, be it by its nature or by design.
In the prior art, systems employing a time-delay discriminator are also classified as being either passive or active, depending on whether the physical phenomenon detectable by sensors is inherent in the observed process, or is imparted (or at least enhanced) by the use of some auxiliary means, such as suitable markers influencing (or ‘modulating’) the process, ultrasonic or radio-frequency radiators, visible light or infrared illuminators, etc.
If x(t) denotes one of the two signals applied to the time-delay discriminator TDD, the other signal y(t) can be expressed asy(t)=Ax(t−Δ)+n(t)where A is a scale factor, Δ denotes an unknown time delay and n(t) represents background noise and other interference.
In some practical applications, even in a no-noise case, the signal y(t) will no longer be a scaled and time-shifted replica of the signal x(t), due to flow turbulence, Doppler effect and/or nonlinear sensor characteristics. In such cases, it is assumed that the additive noise waveform n(t) will also include a component representing the respective distortions of the signal shape.
A conventional technique used to determine the value of unknown time delay Δ is based on crosscorrelating the two wideband signals x(t) and y(t), i.e. by performing the operation
            R      xy        ⁡          (      τ      )        =            1      T        ⁢                  ∫        0        T            ⁢                        x          ⁡                      (                          t              -              τ                        )                          ⁢                  y          ⁡                      (            t            )                          ⁢                                  ⁢                  ⅆ          t                    where the integral is evaluated over the observation interval of duration T and for a range, Δmin<τ<Δmax, of delay values of interest. The value of argument τ that maximises the crosscorrelation function Rxy(τ) provides an estimate of an unknown delay Δ.
In practice, prior to crosscorrelation, the signals x(t) and y(t) may be suitably prefiltered to accentuate frequencies for which the signal-to-noise ratio (SNR) is highest and to attenuate background noise, thus increasing the resulting overall SNR. A crosscorrelator utilizing signal prefiltering is known in the prior art as a generalized crosscorrelator.
The crosscorrelation process, including prefiltering, can also be implemented digitally, if sufficient sampling and quantising of the signal is used.
FIG. 3 is a block diagram of a conventional system crosscorrelating a received signal y(t) with a reference signal x(t) to determine the value of the unknown delay, and FIG. 4 shows an example of a crosscorrelation function Rxy(τ) between a signal x(t) and its replica y(t) delayed by Δ. In this case, the resulting crosscorrelation function Rxy(τ) is the same as a time-shifted autocorrelation function Rxx(τ) of the signal x(t). Because of the symmetry of Rxy(τ) with respect to its maximum occurring at τ=Δ, a single value of the cross-correlation function can only provide information about the absolute value |Δ−Δ0| of time-delay error. Therefore, when a correlator is to be used in a time-delay discriminator, some additional operations will have to be performed in order to obtain a bipolar output related to the time-delay error (Δ−Δ0).
For a finite time interval T, the crosscorrelation curve determined experimentally will usually contain errors associated with random fluctuations in the signals themselves, as well as errors due to noise and interference. As a result, the task of locating the crosscorrelation peak is rather difficult to perform in practical systems. Even when the peak is well defined, its position is usually found by evaluating the crosscorrelation function at several points and calculating corresponding differences to approximate the derivative of the crosscorrelation function. Those additional operations are computationally intensive and inconvenient, especially when the peak-seeking procedure is to be implemented for wideband signals in real time.
It is known that the derivative R′xy(τ)=dRxy(τ)/dτ of a crosscorrelation function Rxy(τ) can be obtained by crosscorrelating a first signal with the derivative of a second signal. Because the derivative of a crosscorrelation function is an odd function, i.e. R′xy(−τ)=−R′xy(τ), it can provide information about the time-delay error. In some crosscorrelator systems, a similar result is achieved by replacing signal differentiation by Hilbert transformation.
Irrespective of the approach, when there is no noise, and the observation time is sufficiently long, the resulting bipolar curve will cross a zero level exactly at the time instant τ equal to the time delay Δ between two signals being processed. FIG. 5 shows an example of a curve observed at the output of a suitably modified crosscorrelator system processing jointly a signal x(t) and its replica y(t) delayed by Δ. Because of the characteristic bipolar S-shape of the curve, such a system can perform the function of a time-delay discriminator required in a delay-locked loop intended to track a time-varying delay of interest.
In general, wideband signals encountered in practical applications are nonstationary with evidently non-Gaussian statistical characteristics. Therefore, many known crosscorrelation techniques based, explicitly or implicitly, on the assumptions of signal stationarity and Gaussianity are only of limited practical use. Furthermore, most practical implementations have to deal with discrete-time samples, so that the optimisation procedures and performance analyses carried out in the continuous-time framework cannot be fully applicable.
WO-A-00/39643 discloses an improved method for the estimation of the time delay between signals using a technique referred to herein as “crosslation”. The contents of WO-A-00/39643 are incorporated herein by reference.
The term “crosslation” as used herein refers to a technique whereby predefined (preferably at least substantially aperiodic) events which occur in one signal are used to define staggered segments of a second signal, and representations of the staggered segments are then combined. The first and second signals may in fact be the same signal, in which case the resulting combined representation will provide information regarding the statistical properties of that signal, and in particular about the average behaviour of the signal before and after the predefined events. Alternatively, the first and second signals may be different signals (“mutual crosslation”), or one signal may be a delayed version of the other, in which case the combined representation will provide information about the relationship between those signals. For example, if the combined representation contains a feature which would be expected from combining segments associated with multiple predefined events, this may indicate that one of the signals is delayed with respect to the other by an amount corresponding to the position within the representation of that feature.
According to WO-A-00/39643, a bipolar signal is subjected to an unknown delay, and the reference (non-delayed) version of the signal is examined to determine the time instants at which its level crosses zero with a positive slope (an upcrossing). The timing of these crossing events is used to obtain respective segments of the delayed signal, the segments having a predetermined duration. The segments are all summed, and a representation of the summed segments is then examined to locate a feature in the form of an S-shaped odd function. The position within the representation of a zero-crossing in the centre of the odd function represents the amount by which the signal has been delayed. Instead of using upcrossings, the reference (non-delayed) version of the signal could be examined to determine when its level crosses zero with a negative slope (downcrossings).
WO-A-00/39643 also suggests improving accuracy by using both upcrossings and downcrossings. In this case, the odd S-shaped function to be examined is obtained by summing segments defined by upcrossings and subtracting those defined by downcrossings.
The crosslation techniques of WO-A-00/39643 are robust and particularly well suited for processing non-Gaussian signals corrupted by non-Gaussian noise. Because only timing instants are extracted from one of the signals, time delay estimators based on crosslation are much less sensitive to nonlinear signal distortions than the many conventional estimators. However, the performance of the crosslation technique in its disclosed form can be degraded in applications involving strongly non-stationary intermittent signals with prominent bursts followed by signal fading.
Accordingly, it would be desirable to provide an improved technique for time delay measurement, for example, for use in a feedback control system incorporating a time-delay discriminator.